LAFC and Galaxy; along with all the other youth teams that are attached to MLS Clubs; do not play the other non-MLS youth teams. The MLS youth teams are in the "Pro Player Pathway" league/bracket and the other teams (LA Surf, Strikers, TFA, etc.) are all in the "Elite Player League/Bracket and only play each other.
That’s not true (at least in U15 and U17 where the Academies field teams in MLS Next). Besides friendlies, one half of the season is called MLS Next Flex, where LA Galaxy and LAFC play the non-MLS teams in MLS Next and the other half of the season is called League and that is where the Academies fly around and play other MLS academies and the non-MLS teams play each other. The non-MLS affiliated teams also play MLS academies from around the country in showcases and playoffs